1st degree and Bachelor-level of the Bologna process in Civil Engineering - Torino1st degree and Bachelor-level of the Bologna process in Architectural Engineering - Torino1st degree and Bachelor-level of the Bologna process in Environmental Engineering - Torino

Main goal of this course is to complete the introduction of the basic topics of mathematical analysis of functions of several variables. In particular, the theory of multiple integration and of surface integration is developed. Furthermore, numerical series and series of functions (power series and Fourier series in particular) and systems of ordinary differential equations are studied.

Expected skills

Familiarity with the subjects of the course and computational ability. Ability to read a technical text.

Prerequisites

The topics of the courses Analisi Matematica 1 and Geometria. In particular: limits of functions and differential calculus for functions of one variable; integrals of functions of one variable and differential equations; linear algebra, eigenvalues and eigenvectors; geometry of curves and surfaces. Continuity of functions of several variables, computation of partial derivatives, differential and jacobian matrix. Minima and maxima of functions of several variables, taken at interior points of the domain.

Integral calculus: multiple integration. Length of a curve and area of a surface. Curve and surface integration. Green, Gauss and Stokes Theorems. Conservative fields and differential forms.

Numerical series and series of functions: definition and criteria for convergence. Power series and Taylor series. Series solutions of ordinary differential equations of the first order. Fourier series in real and complex form: computation of the coefficients and convergence properties.

Systems of differential equations: solutions of linear systems. Qualitative behaviour of the solutions.

Laboratories and/or exercises

Exercises will be made in class.

Bibliography

The following texts are used in the courses of Analisi Matematica 2. Ask your teacher or look at the WEB page of your course for specific information.

The exam consists of a written and of an oral part. The written part ascertains the familiarity of the student with the arguments of the course while the oral part is mostly concerned with the theory.
In order to be admitted to the oral part of the exam, students should score 15/30 or higher in the written part.